A104985 Row sums of triangle A104984.

1, 0, -2, -6, -20, -92, -554, -4002, -33096, -306440, -3135766, -35134670, -427878628, -5628940084, -79572364498, -1203168642362, -19379896959776, -331331041788640, -5993029816637262, -114348894263852326, -2295445815821635932, -48362099044178487564

Offset: 0

Author

Paul D. Hanna, Apr 10 2005

Keywords

• sign

Comments

A104984 equals the matrix inverse of A104980.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A104984, A104980.

Programs

Mathematica

A003319[n_]:= A003319[n]= If[n==0, 0, n! -Sum[j!*A003319[n-j], {j,n-1}]];
A104984[n_, k_]:= If[k==n, 1, If[k==n-1, -n, -A003319[n-k]]];
a[n_]:= Sum[A104984[n, k], {k,0,n}];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jun 07 2021 *)

PARI

{a(n)=sum(k=0,n,if(k==n,1,if(k==n-1,-n, -polcoeff((1-1/sum(i=0,n-k,i!*x^i))/x+O(x^(n-k)),n-k-1) )))}

Sage

@CachedFunction
def T(n,k):
    if (k==n): return 1
    elif (k==n-1): return -n
    else: return -factorial(n-k) - sum( factorial(j)*T(n-k-j, 0) for j in (1..n-k-1) )
[sum(T(n,k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 07 2021

Formula

a(n) = Sum_{k=0..n} A104984(n, k).